I was unable to set the APN using the iPhone Configuration Utility. After creating an adequate configuration profile in the iPhone Configuration Utility, I tried to install it on the iPhone, but the iPhone then displayed the following diagnostic message: "Profile Failed to Install", "Only One APN configuration can be installed at a time". Since then, I have browsed the net extensively to find a solution, but without success.

To your knowledge, does the iPhone iOS allow to set the APN using the iPhone Configuration Utility (without jailbreak)?

i would suggest you try using unlockit or the iPhone Configuration Utility so that you can set the APN again. Once you have the default APN settings from the SIM, it will allow you to install a new APN file. However, i believe it will prevent you from adding an APN file when you already have another custom APN file installed. If this does not work, then try Settings->General.You should see if there is a customer APN installed. Also, this might be under Settings->General->Network. try both.
iPhone 3G, iPhone 4, iPad2, Travel International Motorola (At&t,T-Mobile and SmartFree Quattro) iSip from InTouch SmartCards

Since my post, I was able to connect to Chatr's data network by: (1) doing a "restore" (but not a "restore from a backup") which refreshed the activation policy to Chatr's, then (2) setting Chatr's APN using either the iPhone Configuration Utility or Unlockit NZ. However, after I did a "restore from backup" after the "restore" in order to retrieve my apps and data, I lost Chatr's APN settings as well as the ability to edit the APN.

Since setting the APN (using either the iPhone Configuration Utility or Unlockit NZ) would succeed after "restore" but fail after "restore from a backup", I became convinced that the profile installation failure was caused by an APN setting that came from my previous iPhone (a jailbroken iPhone 3G), that was transfered to my iPhone 4 by the backup I did when I changed phones.

I was able to resolve my problem by doing a "restore" without a backup, and then reloading all apps and app data. Prior to the "restore", I exported all the app data I could via sync or email (I lost the remaining app data), and I made note of my app settings. The process took a while but my phone is fixed.